The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

Chengyang Yi; Yu Zheng

doi:10.1007/s11401-024-0024-6

The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

Chengyang Yi^*
, Yu Zheng^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.

Original language	English
Pages (from-to)	487-496
Number of pages	10
Journal	Chinese Annals of Mathematics. Series B
Volume	45
Issue number	3
DOIs	https://doi.org/10.1007/s11401-024-0024-6
State	Published - May 2024

Keywords

Logarithmic Sobolev inequality
Nonnegative sectional curvature
Submanifold

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10.1007/s11401-024-0024-6

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title = "The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature",

abstract = "The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.",

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doi = "10.1007/s11401-024-0024-6",

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AU - Yi, Chengyang

AU - Zheng, Yu

N1 - Publisher Copyright: © The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024.

PY - 2024/5

Y1 - 2024/5

N2 - The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.

AB - The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.

KW - Logarithmic Sobolev inequality

KW - Nonnegative sectional curvature

KW - Submanifold

UR - https://www.scopus.com/pages/publications/85195120970

U2 - 10.1007/s11401-024-0024-6

DO - 10.1007/s11401-024-0024-6

M3 - 文章

AN - SCOPUS:85195120970

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VL - 45

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EP - 496

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 3

ER -

The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

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Keywords

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